The 28-year-old was linked with a move to Spurs, but manager Harry Redknapp was not impressed by Appiah’s recent trial at the club.
Appiah is out of contract and can join the Russian side for free.
“It is important that I get back to playing actively before the start of the World Cup qualifiers, so I need regular action,” he said on Kick Off Ghana.
“There are other clubs too who are keen, and that goes with my desire to play competitively.”
He added: “The prospect of playing in the Uefa Champions League next season is very attractive to any player so I had to listen to Kazan.
“The fact that Kazan won the league ahead of two big clubs – Lokomotiv and Dynamo – shows that they will take Europe by storm and I am excited.”